Question

Table 2 shows two random independent samples of stock return over 10 years’ time. Assume the rate of return ?_? for stock A and ?_? for stock B are normally distributed with population standard deviation ?? = 0.01 and ?? = 0.02 respectively. To investigate whether the average rate of return for stock A different from the average rate of return for stock B, please answer the following questions.

1. State the null hypothesis and the alternative hypothesis.
2. Select an appropriate test statistic and state its distribution.
3. Calculating the sample mean ?¯_? of the rate of return for stock A and the sample mean ?¯_?  of the rate of return for stock B (show your final answer correct to three decimal places).
4. Calculate the test statistics from the sample (show your final answer correct to two decimal places).
5. (1 mark) If the significant level is 0.1, calculate the critical values.
6. Is the average rate of return for stock A different from the average rate of return for stock B, justify your answer.

	Stock A	Stock B
Year 1	0.04	0.11
Year 2	0.07	0.08
Year 3	0.08	0.12
Year 4	0.13	0.09
Year 5	0.06	0.05
Year 6	0.05	0.03
Year 7	0.05	0.06
Year 8	0.12	0.10
Year 9	0.09	0.07
Year 10	0.03	004

Answer 1

a)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0

b) two mean independnet sample Z test , distribution is normal

c) mean of sample 1,    x̅A=   0.072

mean of sample 2,    x̅B=   0.075

d)

difference in sample means = x̅1 - x̅2 =    0.072   -   0.075   =   -0.003
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    0.0071          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    -0.003   /   0.0071   =   -0.42
                  

e)  Z-critical value , Z* =    ±   1.6449   [excel formula =NORMSINV(α/2)]

f) test stat > -1.645 , fail to reject Ho

There is no enough evidence to conclude that the average rate of return for stock A different from the average rate of return for stock B,